CF1798D Shocking Arrangement

You are given an array $ a_1, a_2, \ldots, a_n $ consisting of integers such that $ a_1 + a_2 + \ldots + a_n = 0 $ . You have to rearrange the elements of the array $ a $ so that the following condition is satisfied: $$\max\limits_{1 \le l \le r \le n} \lvert a_l + a_{l+1} + \ldots + a_r \rvert < \max(a_1, a_2, \ldots, a_n) - \min(a_1, a_2, \ldots, a_n)$$ where $ |x| $ denotes the absolute value of $ x $ .More formally, determine if there exists a permutation $ p_1, p_2, \ldots, p_n $ that for the array $ a_{p_1}, a_{p_2}, \ldots, a_{p_n} $ , the condition above is satisfied, and find the corresponding array.Recall that the array $ p_1, p_2, \ldots, p_n $ is called a permutation if for each integer $ x $ from $ 1 $ to $ n $ there is exactly one $ i $ from $ 1 $ to $ n $ such that $ p_i = x$.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 50\,000 $ ). The description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 300\,000 $ ) — the length of the array $ a $ . The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ -10^9 \le a_i \le 10^9 $ ) — elements of the array $ a $ . It is guaranteed that the sum of the array $ a $ is zero, in other words: $ a_1 + a_2 + \ldots + a_n = 0 $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 300\,000 $ .

For each test case, if it is impossible to rearrange the elements of the array $ a $ in the required way, print "No" in a single line. If possible, print "Yes" in the first line, and then in a separate line $ n $ numbers — elements $ a_1, a_2, \ldots, a_n $ rearranged in a valid order ( $ a_{p_1}, a_{p_2}, \ldots, a_{p_n} $ ). If there are several possible answers, you can output any of them.

In the first test case $ \max(a_1, \ldots, a_n) - \min(a_1, \ldots, a_n) = 9 $ . Therefore, the elements can be rearranged as $ [-5, -2, 3, 4] $ . It is easy to see that for such an arrangement $ \lvert a_l + \ldots + a_r \rvert $ is always not greater than $ 7 $ , and therefore less than $ 9 $ . In the second test case you can rearrange the elements of the array as $ [-3, 2, -3, 2, 2] $ . Then the maximum modulus of the sum will be reached on the subarray $ [-3, 2, -3] $ , and will be equal to $ \lvert -3 + 2 + -3 \rvert = \lvert -4 \rvert = 4 $ , which is less than $ 5 $ . In the fourth test example, any rearrangement of the array $ a $ will be suitable as an answer, including $ [-1, 0, 1] $ .